*Tuesday 1 ^{st} Week*

Video Night

We will be showing a video about the life of Srinivasa Ramanujan,

described by C.P. Snow as “an admirable story”.

*Tuesday 2 ^{nd} Week*

Paul Garcia

*Percy A MacMahon – a good soldier spoiled.*

Major MacMahon was a famous and well respected figure in the

world of late Victorian and Edwardian mathematics. He began his career as

an officer in the Royal Artillery, but was forced by circumstances to

become

a mathematician. A keen billiards player and man-about-town, he wrote over

120 papers and four books, two of which are still in print and cited

regularly. An interest in puzzles led him to patent three of his own, and

write a very unusual book in which he anticipated the work of the Dutch

artist Escher by over a decade. Much of his mathematics was concerned with

Partition Theory, and he almost single-handedly invented modern Combinatory

Analysis.

But he rose to prominence for a discovery in Invariant Theory, so he is

particularly suitable person to be introduced to the Invariant Society.

*Tuesday 3 ^{rd} Week*

Video Night

We will be showing 2 videos, one an introduction to topology and the second on

the four-colour problem.

*Tuesday 4 ^{th} Week*

Marcus Du Sautoy (All Souls)

*The Music of the Primes*

Prime numbers are the atoms of arithmetic – the hydrogen and oxygen

of the world of numbers. Despite their fundamental importance to

mathematics, they represent one of the most tantalising enigmas in the

pursuit of human knowledge. In 1859, the German mathematician Bernhard

Riemann put forward an ideal – a hypothesis – which seemed to reveal a

magical harmony at work in the numerical landscape. A million dollars

now awaits the person who can unravel the mystery of the hidden music

that might explain the cacophany of the primes.

*Tuesday 5 ^{th} Week*

Maxim Vsemirnov (Sidney Sussex College, Cambridge)

*Counting lattice points: Cantor’s polynomials and more*

There are many ways to show that the Cartesian square of a

countable set, say the set of non-negative integers, is countable.

More precisely, there are infinitely many ways to enumerate its

elements. Two of these enumerations have a very nice form: they

are given by polynomials. They were already known to Cantor more

than one hundred years ago.

Are there other pairing polynomials, i.e., polynomials that give a

one-to-one correspondence between pairs of non-negative integers and

non-negative integers? This question looks very natural and simple, but

the complete answer is still not known. Even in the simplest case of

quadratic polynomilas, the original proofs due to Fueter and Polya

(1920-s) were very deep and complicated. An elementary approach was

developed only 5 years ago.

In this talk I will try to explain in an elementary way

the fact that the only quadratic pairing polynomials are those

known to Cantor. No extra knowledge except some basic number theory

is required. At the end, some open problems including higher-dimensional

generalizations will be discussed.

*Thursday 5 ^{th} Week*

Invariants Annual Dinner

*Jesus College*

This will also be an opportunity for those interested in being on next

year’s committee to talk to current committee members. More details

coming soon!

*Tuesday 6 ^{th} Week*

Marc Lackenby (St. Catz)

*“Life in a non-Euclidean world”, followed by AGM*

We are used to the usual Euclidean universe, where the angles

of a triangle add up to 180 degrees, and where parallel lines

stay the same distance from each other. But there are other

richer types of geometry where these familiar notions break

down. The most interesting of these is hyperbolic space, discovered

by Gauss but which he considered too scandalous to publish

to the world. I will explain what it is like to live in hyperbolic

space. It turns out to be a rather unpleasant: it is cold, dark and

easy to get lost in. But it is also the source of a lot of interesting

mathematics, and may be a closer description of our universe

than you might think.

The talk will be followed by our AGM.

*Tuesday 7 ^{th} Week*

Members’ Papers

If you are interested in presenting a paper please contact the secretary

(David Neuman at Jesus College) for further details.

*Tuesday 8 ^{th} Week*

Raymond Flood (Kellogg)

*Isaac Newton: Life, Labours and Legacy*

In this talk the range of Newton’s work, the interaction with his contempories

and the impact that his work has had on science and mathematics will be

discussed.

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